NCERT Solutions for Square roots Class 8 Maths Chapter 6 CBSE Part 2

Question 1
 Find the square of the following numbers.
(i) 32
 (ii) 35
 (iii) 86
 (iv) 93
 (v) 71
 (vi) 46
Answer
1) 32²
We can find the square using direct multiplication
= 32 x 32 = 1024
But above method can be cumbersome to calculate. We  can calculate such values in the another better way f
Since, 32 can be written as (30+2)
So, 32² = (30+2)² = (30+2)(30+2)
Now we know the identity
(a+b)²= a² + b² +2ab
 = 30² + 2 x 30 x 2 + 2²
= 900 + 120  + 4 = 1024
2) (35)² = (30+5)²
Solving on similar lines as above
= 30² + 2 x 30 x 5  + 5²
= 900 + 300 + 25 = 1225
3) 86² = (80 + 6)²
= 80² + 2 x  80 x 6  + 6²
= 6400 + 960 + 36 = 7396
4) 93² = (90+3)²
= 90 ² +2 x 90 x 3  + 3 ²
= 8100 + 540 + 9 = 8649
5) 71 ² = (70 + 1) ²
= 70² +2 x 70 x 1  + 1 x 1
= 4900 + 140 + 1 = 5040 + 1 = 5041
6) 46² = (40+6)²
= 40 ² + 2 x 40 x 6  + 6²
= 1600 + 480 + 36 = 2080 + 36 = 2116

Question: 2
 Write a Pythagorean triplet whose one member is:
(i) 6
 (ii) 14
 (iii) 16
 (iv) 18
Answer
As we know 2n, n ² + 1 and n² - 1 form a Pythagorean triplet for any number, n > 1.
1) If we take n ² + 1 or  n² - 1 to be 6 then then the value of n will  not integer(n²  will be 5 or 7)
So  we can  2n = 6
Therefore, n = 3
And, n² + 1 = 3 ² + 1= 9 + 1 = 10
And,n ² - 1 = 3 ² - 1 = 9 - 1 = 8
Test: 6 ² + 8 ² = 36 + 64 = 100 = 10²
Hence, the triplet is 6, 8, and 10 Answer
2) If we take n ² + 1 or  n² - 1 to be 14 then then the value of n will  not integer(n²  will be 15 or 13)
So we can take 2n= 14, therefore, n = 7
Now, n ² + 1 = 7 ² + 1 = 49 + 1 = 50
And, n² - 1 = 7 ² - 1 = 49 - 1 = 48
Test: 14 ² + 48 ² = 196 + 1304 = 2500 = 50 ²
Hence, the triplet is 14, 48, and 50 Answer
3) If we take n ² + 1 or  n² - 1 to be 16 then then the value of n will  not integer(n²  will be 17 or 15)
Let us assume 2n = 16, then n = 8
Now, n² + 1 = 8 ² + 1 = 64 + 1 = 65
And, n ² - 1 = 8 ² - 1 = 64 - 1 = 63
Test: 16² + 63 ² = 256 + 3969 = 4225 = 65 ²
Hence, the triplet is 16, 63, and 65 Answer
4) If we take n ² + 1 or  n² - 1 to be 18 then then the value of n will  not integer(n²  will be 19 or 17)
Let us assume 2n = 18, therefore, n = 9
Now, n ² + 1 = 9 ² + 1 = 81 + 1 = 82
And, n ² - 1 = 9 ² - 1 = 81 - 1 = 80
Test: 18 ² + 80 ² = 324 + 6400 = 6724 = 82 ²

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Class 8 Maths Class 8 Science